Jackknife methods for left-truncated data

Let U*U* and V*V* be two independent positive random variables with continuous distribution functions F and G  , respectively. Under random truncation, both U*U* and V*V* are observable only when U*≥V*U*≥V*. Let F¯n be the nonparametric maximum likelihood estimate (Lynden-Bell, 1971) of F¯=1−F. In this paper, it is shown that the jackknife variance estimate of F¯n consistently estimates the limit variance. In a simulation study, we show that the jackknife works satisfactorily for moderate sample size. As an illustration we also apply our method to a real set of AIDS data.